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Article Citation - WoS: 146Citation - Scopus: 166On the Solutions of Fractional Differential Equations Via Geraghty Type Hybrid Contractions(Ministry Communications & High Technologies Republic Azerbaijan, 2021) Adiguzel, Rezan Sevinik; Sevinik Adıgüzel, Rezan; Aksoy, Umit; Aksoy, Ümit; Karapinar, Erdal; Karapınar, Erdal; Erhan, Inci M.; Erhan, İnci; Sevinik Adıgüzel, Rezan; Aksoy, Ümit; Karapınar, Erdal; Erhan, İnci; Mathematics; Mathematics; MathematicsThe aim of this article is twofold. Firstly, to study fixed points of mappings on b metric spaces satisfying a general contractive condition called Geraghty type hybrid contraction. Secondly, to apply the theoretical results to the problem of existence and uniqueness of solutions of boundary value problems with integral boundary conditions associated with a certain type of nonlinear fractional differential equations. The conditions for the existence of fixed points for Geraghty type hybrid contractions are determined and several consequences of the main results are deduced. Some examples on boundary value problems for nonlinear fractional differential equations of order 3 < alpha <= 4 are provided, where the existence and uniqueness of solutions are shown by using Geraghty type contractions.Article Citation - WoS: 4Citation - Scopus: 4Generalized (ξ,α )-Expansive Mappings and Related Fixed-Point Theorems(Springeropen, 2014) Karapinar, Erdal; Shahi, Priya; Kaur, Jatinderdeep; Bhatia, Satvinder SinghIn this paper, we introduce a new class of expansive mappings called generalized (xi,alpha)-expansive mappings and investigate the existence of a fixed point for the mappings in this class. We conclude that several fixed-point theorems can be considered as a consequence of main results. Moreover, some examples are given to illustrate the usability of the obtained results.Article Citation - WoS: 5Citation - Scopus: 4Common Coupled Fixed Point Theorems in d-complete Topological Spaces(Duke Univ Press, 2012) Rao, K. P. R.; Rao, K. R. K.; Karapinar, ErdalIn this paper, we give two unique common coupled fixed point theorems for mappings satisfying a generalized condition in d-complete topological spaces.Article Citation - WoS: 21Citation - Scopus: 23Suzuki-Edelstein Type Contractions Via Auxiliary Functions(Hindawi Ltd, 2013) Salimi, Peyman; Karapinar, ErdalWe prove the existence and uniqueness of a fixed point of certain type mapping, extension of Suzuki-Edelstein mapping, in a partially ordered complete metric space. Our results extend, improve, and generalize the existence results on the topic in the literature. We state some examples to illustrate our results.Conference Object Citation - WoS: 2Citation - Scopus: 1Rational Forms That Imply the Uniqueness of Fixed Points in Partial Metric Spaces(Yokohama Publ, 2019) Karapinar, Erdal; MathematicsIn this paper, we investigate the existence and uniqueness of fixed points of Jaggi type contractions by using a simulation function in the framework of partial metric spaces. Our results improve, extend and unify several results on the topic in the literature.Editorial Advances on Multivalued Operators and Related Fixed Point Problems(Hindawi Publishing Corporation, 2014) Chen, Chi-Ming; Karapinar, Erdal; Du, Wei-Shih; Aydi, Hassen; Romaguera, Salvador; Karapnar, Erdal[No Abstract Available]Article Citation - WoS: 64Citation - Scopus: 78Fixed Points for Generalized (α, Ψ)-Contractions on Generalized Metric Spaces(Springeropen, 2014) Aydi, Hassen; Karapinar, Erdal; Samet, BessemIn this paper, we introduce some generalized (alpha, psi)-contractive mappings in the setting of generalized metric spaces and, based on the very recent paper (Kirk and Shahzad in Fixed Point Theory Appl. 2013:129, 2013), we omit the Hausdorff hypothesis to prove some fixed point results involving such mappings. Some consequences on existing fixed point theorems are also derived.Article Citation - WoS: 5Citation - Scopus: 11Remarks on Some Recent Fixed Point Results on Quaternion-Valued Metric Spaces(Hindawi Ltd, 2014) Agarwal, Ravi P.; Alsulami, Hamed H.; Karapinar, Erdal; Khojasteh, FarshidVery recently, Ahmed et al. introduced the notion of quaternion-valued metric as a generalization of metric and proved a common fixed point theorem in the context of quaternion-valued metric space. In this paper, we will show that the quaternion-valued metric spaces are subspaces of cone metric spaces. Consequently, the fixed point results in such spaces can be derived as a consequence of the corresponding existing fixed point result in the setting cone metric spaces.Book Part Citation - WoS: 1Citation - Scopus: 2A Fixed Point Result on the Interesting Abstract Space: Partial Metric Spaces(Springer international Publishing Ag, 2019) Karapinar, ErdalIn this chapter, we shall investigate the existence of fixed point of certain mappings via simulation functions in the framework of an interesting abstract space, namely, partial metric spaces. The main results of this manuscript not only extend, but also generalize, improve and unify several existing results on the literature of metric fixed point theory.Article Citation - WoS: 20Citation - Scopus: 28Some Extensions for Geragthy Type Contractive Mappings(Springer international Publishing Ag, 2015) Karapinar, Erdal; Alsulami, Hamed H.; Noorwali, MahaIn this paper, we establish some fixed point theorems on some extensions of Geragthy contractive type mappings in the context of b-metric-like spaces.
